Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
456 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10617444 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | D5×#510 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #10604859 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #10604852 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×#64910 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10598676 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10598672 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #66264 | — | 2 | 1 | no | — |
| 9 | D5×#135 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×D5×Q16 | C22 | 1 | 1 | yes | characteristic |
| 11 | #65795 | — | 2 | 1 | no | — |
| 12 | D5⋊#101 | — | 2 | 1 | no | — |
| 13 | #65782 | — | 2 | 1 | no | — |
| 14 | #65741 | — | 2 | 1 | no | — |
| 15 | #65736 | — | 2 | 2 | no | — |
| 16 | #65733 | — | 2 | 1 | no | — |
| 17 | D5⋊#108 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#3995 | C22 | 1 | 1 | yes | characteristic |
| 19 | #65718 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#3990 | C22 | 1 | 1 | yes | characteristic |
| 21 | C5×#510 | C4 | 1 | 1 | yes | characteristic, complemented |
| 22 | #65484 | C4 | 1 | 1 | yes | characteristic, complemented |
| 23 | #65468 | C4 | 1 | 1 | yes | characteristic, complemented |
| 24 | #65207 | — | 2 | 1 | no | — |
| 25 | D5×Q32 | — | 2 | 1 | no | — |
| 26 | #65204 | — | 2 | 1 | no | — |
| 27 | D5×SD32 | — | 2 | 1 | no | — |
| 28 | #65198 | C4 | 1 | 1 | yes | characteristic, complemented |
| 29 | D5×M32 | C22 | 1 | 1 | yes | characteristic |
| 30 | #64910 | — | 2 | 1 | no | — |
| 31 | #64910 | — | 2 | 2 | no | — |
| 32 | #64906 | — | 2 | 1 | no | — |
| 33 | #13031 | — | 5 | 1 | no | maximal, Sylow |
| 34 | D5×#41 | — | 2 | 1 | no | — |
| 35 | C2×Q8×D5 | — | 2 | 1 | no | — |
| 36 | #4133 | — | 2 | 2 | no | — |
| 37 | #4131 | — | 2 | 2 | no | — |
| 38 | #4131 | — | 4 | 2 | no | — |
| 39 | #4130 | D4 | 1 | 1 | yes | characteristic |
| 40 | D5⋊M16 | — | 2 | 1 | no | — |
| 41 | D5⋊M16 | — | 4 | 1 | no | — |
| 42 | D5⋊M16 | D4 | 1 | 1 | yes | characteristic |
| 43 | C2×#700 | — | 2 | 1 | no | — |
| 44 | C2×#700 | — | 4 | 1 | no | — |
| 45 | C5×#135 | C2×C4 | 1 | 1 | yes | characteristic |
| 46 | C2×C5×Q16 | C2×C4 | 1 | 1 | yes | characteristic |
| 47 | #4096 | — | 2 | 1 | no | — |
| 48 | C2×#689 | — | 2 | 1 | no | — |
| 49 | #4065 | D4 | 1 | 1 | yes | characteristic |
| 50 | D5×Q16 | — | 2 | 1 | no | — |
| 51 | D5×Q16 | — | 2 | 1 | no | — |
| 52 | D5×Q16 | — | 2 | 1 | no | — |
| 53 | D5×Q16 | — | 2 | 1 | no | — |
| 54 | D5×Q16 | D4 | 1 | 1 | yes | characteristic |
| 55 | #4062 | — | 2 | 1 | no | — |
| 56 | D5×SD16 | — | 2 | 1 | no | — |
| 57 | #4058 | D4 | 1 | 1 | yes | characteristic |
| 58 | D5×D8 | D4 | 1 | 1 | yes | characteristic |
| 59 | C2×Dic20 | C2×C4 | 1 | 1 | yes | characteristic |
| 60 | #4050 | C2×C4 | 1 | 1 | yes | characteristic |
| 61 | C2×C8×D5 | C23 | 1 | 1 | yes | characteristic |
| 62 | #4010 | — | 2 | 2 | no | — |
| 63 | #4009 | — | 4 | 2 | no | — |
| 64 | #4008 | — | 2 | 2 | no | — |
| 65 | #4005 | — | 4 | 2 | no | — |
| 66 | C2×#674 | — | 2 | 1 | no | — |
| 67 | #3996 | — | 2 | 1 | no | — |
| 68 | #3995 | — | 2 | 1 | no | — |
| 69 | #3995 | — | 2 | 1 | no | — |
| 70 | #3995 | D4 | 1 | 2 | yes | — |
| 71 | #3992 | — | 2 | 1 | no | — |
| 72 | C8×AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 73 | #3990 | — | 2 | 1 | no | — |
| 74 | #3990 | — | 2 | 1 | no | — |
| 75 | C5×Q32 | — | 2 | 1 | no | — |
| 76 | C5×SD32 | — | 2 | 1 | no | — |
| 77 | C5×M32 | C2×C4 | 1 | 1 | yes | characteristic |
| 78 | #3961 | — | 2 | 1 | no | — |
| 79 | #3961 | — | 2 | 1 | no | — |
| 80 | #3960 | — | 2 | 1 | no | — |
| 81 | #3959 | — | 2 | 1 | no | — |
| 82 | #3944 | C2×C4 | 1 | 1 | yes | characteristic |
| 83 | Dic40 | — | 2 | 1 | no | — |
| 84 | #3932 | — | 2 | 1 | no | — |
| 85 | #3930 | — | 2 | 1 | no | — |
| 86 | D5×C16 | — | 2 | 1 | no | — |
| 87 | C2×#510 | — | 5 | 1 | no | — |
| 88 | #2957 | — | 5 | 1 | no | — |
| 89 | #2148 | — | 5 | 1 | no | — |
| 90 | C2×#362 | — | 5 | 1 | no | — |
| 91 | #1979 | — | 5 | 1 | no | — |
| 92 | #1388 | — | 5 | 1 | no | — |
| 93 | #1378 | — | 5 | 1 | no | — |
| 94 | C5×#41 | — | 2 | 1 | no | — |
| 95 | C2×C5×Q8 | — | 2 | 1 | no | — |
| 96 | #713 | — | 2 | 1 | no | — |
| 97 | Q8×D5 | — | 2 | 1 | no | — |
| 98 | Q8×D5 | — | 4 | 1 | no | — |
| 99 | Q8×D5 | — | 4 | 1 | no | — |
| 100 | Q8×D5 | — | 4 | 1 | no | — |
| 101 | Q8×D5 | — | 4 | 1 | no | — |
| 102 | #711 | — | 2 | 1 | no | — |
| 103 | #711 | — | 4 | 1 | no | — |
| 104 | D4×D5 | — | 2 | 1 | no | — |
| 105 | D4×D5 | — | 4 | 1 | no | — |
| 106 | #709 | — | 2 | 1 | no | — |
| 107 | #709 | — | 4 | 1 | no | — |
| 108 | C2×C4×D5 | — | 4 | 1 | no | — |
| 109 | C2×C4×D5 | — | 4 | 1 | no | — |
| 110 | C2×C4×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 111 | C2×Dic10 | — | 2 | 1 | no | — |
| 112 | C2×Dic10 | — | 4 | 1 | no | — |
| 113 | C22⋊AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 114 | #704 | — | 4 | 2 | no | — |
| 115 | #704 | — | 4 | 1 | no | — |
| 116 | #704 | D8 | 1 | 2 | yes | — |
| 117 | C2×#170 | — | 4 | 2 | no | — |
| 118 | C2×#170 | — | 4 | 1 | no | — |
| 119 | C4⋊AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 120 | C4×AGL(1,𝔽5) | — | 2 | 1 | no | — |
| 121 | #700 | — | 2 | 1 | no | — |
| 122 | #700 | — | 2 | 2 | no | — |
| 123 | #700 | — | 4 | 2 | no | — |
| 124 | #700 | — | 4 | 1 | no | — |
| 125 | #700 | — | 4 | 1 | no | — |
| 126 | D5⋊C8 | — | 2 | 1 | no | — |
| 127 | D5⋊C8 | — | 4 | 2 | no | — |
| 128 | D5⋊C8 | — | 4 | 1 | no | — |
| 129 | C5×Q16 | — | 2 | 1 | no | — |
| 130 | C5×Q16 | — | 2 | 1 | no | — |
| 131 | C5×Q16 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 132 | C5×SD16 | — | 2 | 1 | no | — |
| 133 | C5×D8 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 134 | C2×C5×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 135 | #689 | — | 2 | 1 | no | — |
| 136 | #689 | — | 4 | 1 | no | — |
| 137 | #689 | — | 4 | 1 | no | — |
| 138 | #688 | — | 2 | 1 | no | — |
| 139 | #687 | — | 2 | 1 | no | — |
| 140 | #686 | — | 2 | 1 | no | — |
| 141 | C2×#168 | #41 | 1 | 1 | yes | characteristic |
| 142 | Dic20 | — | 2 | 1 | no | — |
| 143 | Dic20 | — | 2 | 1 | no | — |
| 144 | Dic20 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 145 | D40 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 146 | #677 | — | 2 | 1 | no | — |
| 147 | C8×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 148 | C8×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 149 | C8×D5 | C2×D4 | 1 | 1 | yes | characteristic |
| 150 | C8×D5 | #41 | 1 | 1 | yes | characteristic |
| 151 | #674 | — | 4 | 1 | no | — |
| 152 | C5×C16 | — | 2 | 1 | no | — |
| 153 | #672 | — | 2 | 1 | no | — |
| 154 | C2×#135 | — | 5 | 1 | no | — |
| 155 | C22×Q16 | — | 5 | 1 | no | — |
| 156 | #568 | — | 10 | 1 | no | — |
| 157 | #510 | — | 5 | 1 | no | — |
| 158 | #510 | — | 5 | 1 | no | — |
| 159 | #510 | — | 5 | 1 | no | — |
| 160 | #510 | — | 10 | 1 | no | — |
| 161 | #510 | — | 10 | 1 | no | — |
| 162 | #510 | AGL(1,𝔽5) | 1 | 1 | yes | characteristic, complemented |
| 163 | C2×Q32 | — | 10 | 1 | no | — |
| 164 | C2×SD32 | — | 10 | 1 | no | — |
| 165 | C2×M32 | — | 5 | 1 | no | — |
| 166 | C2×M32 | — | 5 | 1 | no | — |
| 167 | #444 | — | 10 | 1 | no | — |
| 168 | #444 | — | 10 | 1 | no | — |
| 169 | #443 | — | 10 | 2 | no | — |
| 170 | C2×#108 | — | 5 | 1 | no | — |
| 171 | C2×#108 | — | 5 | 1 | no | — |
| 172 | #421 | — | 10 | 1 | no | — |
| 173 | #419 | — | 10 | 1 | no | — |
| 174 | C2×#101 | — | 10 | 1 | no | — |
| 175 | #405 | — | 5 | 1 | no | — |
| 176 | #362 | — | 10 | 2 | no | — |
| 177 | #362 | — | 10 | 1 | no | — |
| 178 | #361 | — | 10 | 1 | no | — |
| 179 | C22×D5 | — | 4 | 1 | no | — |
| 180 | C22×D5 | #135 | 1 | 1 | yes | characteristic |
| 181 | C2×AGL(1,𝔽5) | — | 4 | 1 | no | — |
| 182 | C5×Q8 | — | 2 | 1 | no | — |
| 183 | C5×Q8 | — | 4 | 1 | no | — |
| 184 | C5×Q8 | — | 4 | 1 | no | — |
| 185 | C5×D4 | — | 2 | 1 | no | — |
| 186 | C5×D4 | — | 4 | 1 | no | — |
| 187 | C2×C4×C5 | — | 4 | 1 | no | — |
| 188 | C2×C4×C5 | — | 4 | 1 | no | — |
| 189 | C2×C4×C5 | C4×D4 | 1 | 1 | yes | characteristic |
| 190 | C22⋊D5 | — | 4 | 1 | no | — |
| 191 | C22⋊D5 | — | 4 | 1 | no | — |
| 192 | C22⋊D5 | — | 4 | 1 | no | — |
| 193 | C2×Dic5 | — | 4 | 1 | no | — |
| 194 | C2×Dic5 | — | 4 | 1 | no | — |
| 195 | C2×Dic5 | C2×D8 | 1 | 1 | yes | characteristic |
| 196 | D20 | — | 2 | 1 | no | — |
| 197 | D20 | — | 4 | 1 | no | — |
| 198 | C4×D5 | — | 4 | 1 | no | — |
| 199 | C4×D5 | — | 4 | 1 | no | — |
| 200 | C4×D5 | — | 4 | 1 | no | — |
| 201 | C4×D5 | — | 8 | 1 | no | — |
| 202 | C4×D5 | — | 8 | 1 | no | — |
| 203 | C4×D5 | #120 | 1 | 1 | yes | characteristic |
| 204 | C4×D5 | #121 | 1 | 1 | yes | characteristic |
| 205 | C4×D5 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 206 | C4×D5 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 207 | Dic10 | — | 2 | 1 | no | — |
| 208 | Dic10 | — | 4 | 1 | no | — |
| 209 | Dic10 | — | 4 | 1 | no | — |
| 210 | Dic10 | — | 4 | 1 | no | — |
| 211 | Dic10 | — | 8 | 1 | no | — |
| 212 | Dic10 | — | 8 | 1 | no | — |
| 213 | #170 | — | 2 | 2 | no | — |
| 214 | #170 | — | 4 | 2 | no | — |
| 215 | #170 | — | 8 | 1 | no | — |
| 216 | C5×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 217 | C5×C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 218 | #168 | #121 | 1 | 1 | yes | characteristic |
| 219 | #168 | #123 | 1 | 1 | yes | characteristic |
| 220 | C2×#41 | — | 10 | 1 | no | — |
| 221 | C22×Q8 | — | 10 | 1 | no | — |
| 222 | #135 | — | 5 | 1 | no | — |
| 223 | #135 | — | 5 | 1 | no | — |
| 224 | #135 | — | 5 | 1 | no | — |
| 225 | #135 | — | 10 | 1 | no | — |
| 226 | #135 | — | 10 | 1 | no | — |
| 227 | #135 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 228 | C2×Q16 | — | 5 | 1 | no | — |
| 229 | C2×Q16 | — | 5 | 1 | no | — |
| 230 | C2×Q16 | — | 10 | 1 | no | — |
| 231 | C2×Q16 | — | 10 | 1 | no | — |
| 232 | C2×Q16 | — | 10 | 1 | no | — |
| 233 | C2×Q16 | — | 10 | 1 | no | — |
| 234 | C2×Q16 | — | 10 | 1 | no | — |
| 235 | C2×Q16 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 236 | C2×SD16 | — | 10 | 1 | no | — |
| 237 | C2×D8 | — | 5 | 1 | no | — |
| 238 | #131 | — | 10 | 2 | no | — |
| 239 | #131 | — | 10 | 2 | no | — |
| 240 | #131 | — | 20 | 2 | no | — |
| 241 | C2×M16 | — | 5 | 1 | no | — |
| 242 | C2×M16 | — | 10 | 1 | no | — |
| 243 | C2×M16 | — | 10 | 1 | no | — |
| 244 | C2×M16 | — | 20 | 1 | no | — |
| 245 | C2×M16 | — | 20 | 1 | no | — |
| 246 | C22×C8 | — | 5 | 1 | no | — |
| 247 | #117 | — | 5 | 1 | no | — |
| 248 | Q32 | — | 2 | 1 | no | — |
| 249 | Q32 | — | 10 | 1 | no | — |
| 250 | Q32 | — | 10 | 1 | no | — |
| 251 | Q32 | — | 10 | 1 | no | — |
| 252 | SD32 | — | 2 | 1 | no | — |
| 253 | SD32 | — | 10 | 1 | no | — |
| 254 | SD32 | — | 10 | 1 | no | — |
| 255 | SD32 | — | 10 | 1 | no | — |
| 256 | M32 | — | 5 | 1 | no | — |
| 257 | M32 | — | 10 | 1 | no | — |
| 258 | M32 | — | 10 | 1 | no | — |
| 259 | M32 | — | 10 | 1 | no | — |
| 260 | M32 | C2×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 261 | C2×C16 | — | 10 | 1 | no | — |
| 262 | C2×C16 | — | 10 | 1 | no | — |
| 263 | #108 | — | 5 | 2 | no | — |
| 264 | #108 | — | 10 | 1 | no | — |
| 265 | #108 | — | 10 | 1 | no | — |
| 266 | #108 | — | 10 | 1 | no | — |
| 267 | #104 | — | 10 | 2 | no | — |
| 268 | #104 | — | 10 | 2 | no | — |
| 269 | #103 | — | 20 | 2 | no | — |
| 270 | #101 | — | 20 | 2 | no | — |
| 271 | #97 | — | 10 | 1 | no | — |
| 272 | C4×C8 | — | 10 | 1 | no | — |
| 273 | C22×C5 | — | 4 | 1 | no | — |
| 274 | C22×C5 | C4×D8 | 1 | 1 | yes | characteristic |
| 275 | C2×D5 | — | 4 | 1 | no | — |
| 276 | C2×D5 | — | 4 | 1 | no | — |
| 277 | C2×D5 | — | 16 | 1 | no | — |
| 278 | C2×D5 | #449 | 1 | 1 | yes | characteristic |
| 279 | C2×D5 | #463 | 1 | 1 | yes | characteristic |
| 280 | AGL(1,𝔽5) | — | 8 | 1 | no | — |
| 281 | C4×C5 | — | 4 | 1 | no | — |
| 282 | C4×C5 | — | 8 | 1 | no | — |
| 283 | C4×C5 | #386 | 1 | 1 | yes | characteristic |
| 284 | C4×C5 | #442 | 1 | 1 | yes | characteristic |
| 285 | Dic5 | — | 4 | 1 | no | — |
| 286 | Dic5 | — | 8 | 1 | no | — |
| 287 | Dic5 | #447 | 1 | 1 | yes | characteristic |
| 288 | Dic5 | #459 | 1 | 1 | yes | characteristic |
| 289 | #41 | — | 2 | 1 | no | — |
| 290 | #41 | — | 10 | 1 | no | — |
| 291 | #41 | — | 10 | 1 | no | — |
| 292 | #41 | — | 10 | 1 | no | — |
| 293 | #41 | — | 20 | 1 | no | — |
| 294 | #41 | — | 20 | 1 | no | — |
| 295 | C2×Q8 | — | 2 | 1 | no | — |
| 296 | C2×Q8 | — | 10 | 1 | no | — |
| 297 | C2×Q8 | — | 10 | 1 | no | — |
| 298 | C2×Q8 | — | 20 | 1 | no | — |
| 299 | C2×Q8 | — | 20 | 1 | no | — |
| 300 | C2×Q8 | — | 20 | 1 | no | — |
| 301 | C2×Q8 | — | 20 | 1 | no | — |
| 302 | C2×Q8 | — | 20 | 1 | no | — |
| 303 | C2×D4 | — | 10 | 1 | no | — |
| 304 | C2×D4 | — | 20 | 1 | no | — |
| 305 | C22×C4 | — | 5 | 1 | no | — |
| 306 | C22×C4 | — | 20 | 1 | no | — |
| 307 | C22×C4 | — | 20 | 1 | no | — |
| 308 | Q16 | — | 2 | 1 | no | — |
| 309 | Q16 | — | 2 | 1 | no | — |
| 310 | Q16 | — | 5 | 1 | no | — |
| 311 | Q16 | — | 10 | 1 | no | — |
| 312 | Q16 | — | 10 | 1 | no | — |
| 313 | Q16 | — | 10 | 1 | no | — |
| 314 | Q16 | — | 20 | 1 | no | — |
| 315 | Q16 | — | 20 | 1 | no | — |
| 316 | Q16 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 317 | SD16 | — | 2 | 1 | no | — |
| 318 | SD16 | — | 10 | 1 | no | — |
| 319 | SD16 | — | 10 | 1 | no | — |
| 320 | SD16 | — | 10 | 1 | no | — |
| 321 | D8 | — | 5 | 1 | no | — |
| 322 | D8 | — | 10 | 1 | no | — |
| 323 | D8 | C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 324 | M16 | — | 5 | 2 | no | — |
| 325 | M16 | — | 10 | 1 | no | — |
| 326 | M16 | — | 10 | 2 | no | — |
| 327 | M16 | — | 20 | 2 | no | — |
| 328 | M16 | — | 20 | 2 | no | — |
| 329 | M16 | — | 20 | 1 | no | — |
| 330 | M16 | — | 20 | 1 | no | — |
| 331 | M16 | — | 20 | 1 | no | — |
| 332 | C2×C8 | — | 5 | 1 | no | — |
| 333 | C2×C8 | — | 5 | 1 | no | — |
| 334 | C2×C8 | — | 5 | 1 | no | — |
| 335 | C2×C8 | — | 5 | 1 | no | — |
| 336 | C2×C8 | — | 5 | 1 | no | — |
| 337 | C2×C8 | — | 10 | 1 | no | — |
| 338 | C2×C8 | — | 20 | 2 | no | — |
| 339 | C2×C8 | — | 20 | 2 | no | — |
| 340 | C2×C8 | — | 20 | 1 | no | — |
| 341 | C2×C8 | — | 20 | 1 | no | — |
| 342 | C2×C8 | C22×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 343 | C4⋊C4 | — | 10 | 1 | no | — |
| 344 | C22⋊C4 | — | 10 | 1 | no | — |
| 345 | C42 | — | 10 | 1 | no | — |
| 346 | C16 | — | 2 | 1 | no | — |
| 347 | C16 | — | 10 | 1 | no | — |
| 348 | C16 | — | 20 | 1 | no | — |
| 349 | C2×C5 | — | 2 | 1 | no | — |
| 350 | C2×C5 | — | 8 | 1 | no | — |
| 351 | C2×C5 | #1879 | 1 | 1 | yes | characteristic |
| 352 | D5 | — | 2 | 1 | no | — |
| 353 | D5 | — | 2 | 1 | no | — |
| 354 | D5 | — | 8 | 1 | no | — |
| 355 | C23 | — | 5 | 1 | no | — |
| 356 | C23 | — | 20 | 1 | no | — |
| 357 | Q8 | — | 2 | 1 | no | — |
| 358 | Q8 | — | 4 | 1 | no | — |
| 359 | Q8 | — | 4 | 1 | no | — |
| 360 | Q8 | — | 10 | 1 | no | — |
| 361 | Q8 | — | 20 | 1 | no | — |
| 362 | Q8 | — | 20 | 1 | no | — |
| 363 | Q8 | — | 20 | 1 | no | — |
| 364 | Q8 | — | 40 | 1 | no | — |
| 365 | Q8 | — | 40 | 1 | no | — |
| 366 | D4 | — | 2 | 1 | no | — |
| 367 | D4 | — | 4 | 1 | no | — |
| 368 | D4 | — | 10 | 1 | no | — |
| 369 | D4 | — | 20 | 1 | no | — |
| 370 | D4 | — | 20 | 1 | no | — |
| 371 | D4 | — | 20 | 1 | no | — |
| 372 | D4 | — | 20 | 1 | no | — |
| 373 | C2×C4 | — | 4 | 1 | no | — |
| 374 | C2×C4 | — | 4 | 1 | no | — |
| 375 | C2×C4 | — | 5 | 1 | no | — |
| 376 | C2×C4 | — | 5 | 1 | no | — |
| 377 | C2×C4 | — | 5 | 1 | no | — |
| 378 | C2×C4 | — | 5 | 1 | no | — |
| 379 | C2×C4 | — | 5 | 1 | no | — |
| 380 | C2×C4 | — | 20 | 1 | no | — |
| 381 | C2×C4 | — | 20 | 1 | no | — |
| 382 | C2×C4 | — | 20 | 1 | no | — |
| 383 | C2×C4 | — | 20 | 1 | no | — |
| 384 | C2×C4 | — | 20 | 1 | no | — |
| 385 | C2×C4 | — | 20 | 1 | no | — |
| 386 | C2×C4 | — | 40 | 1 | no | — |
| 387 | C2×C4 | — | 40 | 1 | no | — |
| 388 | C2×C4 | D4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 389 | C8 | — | 5 | 1 | no | — |
| 390 | C8 | — | 5 | 1 | no | — |
| 391 | C8 | — | 10 | 2 | no | — |
| 392 | C8 | — | 20 | 2 | no | — |
| 393 | C8 | — | 40 | 1 | no | — |
| 394 | C8 | D4×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 395 | C8 | C2×C22⋊AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 396 | C5 | #13031 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 397 | C22 | — | 4 | 1 | no | — |
| 398 | C22 | — | 5 | 1 | no | — |
| 399 | C22 | — | 5 | 1 | no | — |
| 400 | C22 | — | 20 | 1 | no | — |
| 401 | C22 | — | 20 | 1 | no | — |
| 402 | C22 | — | 80 | 1 | no | — |
| 403 | C22 | D8×AGL(1,𝔽5) | 1 | 1 | yes | characteristic |
| 404 | C4 | — | 4 | 1 | no | — |
| 405 | C4 | — | 5 | 1 | no | — |
| 406 | C4 | — | 5 | 1 | no | — |
| 407 | C4 | — | 8 | 1 | no | — |
| 408 | C4 | — | 20 | 1 | no | — |
| 409 | C4 | — | 40 | 1 | no | — |
| 410 | C4 | — | 40 | 1 | no | — |
| 411 | C4 | #65731 | 1 | 1 | yes | characteristic |
| 412 | C4 | #65779 | 1 | 1 | yes | characteristic |
| 413 | C2 | — | 2 | 1 | no | — |
| 414 | C2 | — | 8 | 1 | no | — |
| 415 | C2 | — | 10 | 1 | no | — |
| 416 | C2 | — | 10 | 1 | no | — |
| 417 | C2 | — | 40 | 1 | no | — |
| 418 | C2 | #10604799 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #10604852 | C2 | semidirect |
| 5. C2×#64910 | C2 | semidirect |
| 6. #10598676 | C2 | semidirect |
| 7. #10598672 | C2 | semidirect |
| 21. C5×#510 | C4 | semidirect |
| 22. #65484 | C4 | semidirect |
| 23. #65468 | C4 | semidirect |
| 28. #65198 | C4 | semidirect |
| 162. #510 | AGL(1,𝔽5) | semidirect |
| 396. C5 | #13031 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617444 | 2 |
| D5×#510 | 2 |
| #10604859 | 2 |
| #10604852 | 2 |
| C2×#64910 | 2 |
| #10598676 | 2 |
| #10598672 | 2 |
| #13031 | 5 |